Modeling of the ground plane in electrostatic BEM analysis of MEMS and NEMS

This paper is concerned with calculation of charge distribution on conducting elements in microelectromechanical and nanoelectromechanical systems (MEMS and NEMS). The conductors are beam like in MEMS or nanotubes in NEMS. The ground plane is typically present in such problems. This is usually modeled by constructing image elements with the ground treated as a flat mirror, thereby doubling the size of a problem. An alternative approach is to model the ground directly in a boundary element method (BEM) formulation of the problem. The latter approach is adopted in this paper. The governing BEM equations, and their regularization, is discussed in detail. Numerical results are presented for selected examples and their results are compared with analytical solutions whenever possible.